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**Unformatted text preview: **Introduction to Applied Econometrics Final Do not turn page until told to do so! Name: ID & TA: Richard Walker, Winter 2010 Introduction to Applied Econometrics Richard Walker, Winter 2010 Final Name: ID & TA: (100points) Answer all questions, using the spaces provided. There is room for doodling at the back. 25pts 1. I am investigating the determinants of educational attainment, measured by years of schooling S . I suspect the true data-generating process is given by:. S i = β 1 + β 2 BRAINS i + β 3 SM i + β 4 SF i + u i (1) The educational attainment of individual i thus depends on her innate intelligence BRAINS i , on her mother’s years of schooling SM i and on her father’s years of schooling SF i . I have data on S , SM and SF but not on BRAINS , which is unobservable. I do have data on each individual’s score on an intelligence test, IQ i . (a) (15pts) Suppose IQ is only an imperfect proxy for BRAINS . The relationship between the two is given by: IQ i = α 1 + α 2 BRAINS i + i (2) where α 1 and α 2 are unknown positive parameters and i is an error term. I consider using OLS to estimate β 2 in (1), with IQ in place of BRAINS . Show that assumption B7 is violated if I do this. Be sure explicitly to state this assumption. What would be the consequences of using IQ as a proxy for BRAINS in this manner? 25pts 281/final – Page 3 of 12 – Name: (b) (10pts) Now assume instead that IQ is a perfect proxy for BRAINS , i.e. the following equation holds: IQ i = α 1 + α 2 BRAINS i (3) I want to test the null hypothesis that mother’s and father’s years of schooling are equally important for an individual’s own educational attainment, i.e. H : β 3 = β 4 . Derive a regression equation that I can estimate given the available data, and which I can use to test this null hypothesis...

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